Optical communication systems are known in which optical signals carrying data are transmitted from a first node (e.g., a transmitter (Tx)) to a second node (e.g., a receiver (Rx)) via an optical fiber. At the Rx, the optical signal is converted into corresponding electrical signals, which are then further processed.
In some cases, the Rx may include a coherent Rx. In a coherent Rx, a received signal is mixed with an output of a local oscillator (LO) in an optical hybrid circuit, the outputs of which are provided to photodetectors to generate analog electrical output signals. For example, the analog signals may be sampled at a sample rate by analog-to-digital converter (ADC) circuits configured to supply outputs for further processing by a digital signal processor (DSP) included in the coherent Rx. Thus, for the coherent Rx, the amplitude, phase, and state of polarization of the optical signal are all transferred to the electrical domain for digital signal processing in the Rx DSP component.
While travelling through the fiber (e.g., from the Tx to the Rx), the optical signal may be subject to impairments such as chromatic dispersion (CD), polarization mode dispersion (PMD), etc. CD may be caused by various frequency components in each signal traveling at different velocities. PMD may be caused by various polarization components in each signal traveling at different velocities. As a result of such impairments, the in-phase component and quadrature component of electronic signals, representative of data carried by the optical signal, may have different delay, frequency response, and polarization characteristics. PMD and CD compensation may be achieved electronically using an equalizer in the receiver.
For example, the equalizer may be a finite-impulse response (FIR) digital filter. Such filters include taps, where symbols, associated with the signal, are transferred from one tap to the next, multiplied by a coefficient at each tap, and the resulting products are summed. Typically, the coefficients are selected and/or modified based on parameters, such as estimates of CD, PMD, etc., where such estimates may be obtained by “training” the equalizer. One known method of training an equalizer is known as blind equalization. According to the blind equalization method, the equalizer may be trained based on measuring the actual received signal output from the equalizer. One known method of implementing blind equalization is use of a constant modulus algorithm (CMA). In accordance with CMA, filter coefficients are selected and modified through an iterative process, whereby a cost function (e.g., a function associated with an amplitude variation associated with the signal) is minimized.